This invention is in the field of digital communications, and is more specifically directed to Digital Subscriber Line (DSL) communications.
An important and now popular modulation standard for DSL communication is Discrete Multitone (DMT). According to DMT technology, the available spectrum is subdivided into many subchannels (e.g., 256 subchannels of 4.3125 kHz). Each subchannel is centered about a carrier frequency that is phase and amplitude modulated, typically by Quadrature Amplitude Modulation (QAM), in which each symbol value is represented by a point in the complex plane; the number of available symbol values depends, of course, on the number of bits in each symbol. During initialization of a DMT communications session, the number of bits per symbol for each subchannel (i.e., the “bit loading”) is determined according to the noise currently present in the transmission channel at each subchannel frequency and according to the transmit signal attenuation at that frequency. For example, relatively noise-free subchannels may communicate data in ten-bit to fifteen-bit symbols corresponding to a relatively dense QAM constellation (with short distances between points in the constellation), while noisy channels may be limited to only two or three bits per symbol (to allow a greater distance between adjacent points in the QAM constellation). Indeed, some subchannels may not be loaded with any bits, because of the noise and attenuation in those channels. In this way, DMT maximizes the data rate for each subchannel for a given noise condition, permitting high speed access to be carried out even over relatively noisy twisted-pair lines.
DMT modulation also permits much of the processing of the data to be carried out in the digital domain. Typically, the incoming bitstream is serially received and then arranged into symbols, one for each subchannel (depending on the bit loading). Reed-Solomon coding and other coding techniques are also typically applied for error detection and correction. Modulation of the subchannel carriers is obtained by application of an inverse Discrete Fourier Transform (IDFT) to the encoded symbols, producing the output modulated time domain signal. This modulated signal is then serially transmitted. All of these operations in DMT modulation can be carried out in the digital domain, permitting implementation of much of a DSL modem, and particularly much of the processing-intensive operations, in a single chip (such as a Digital Signal Processor, or DSP).
The discrete output time domain signal from the modulation is then converted into a time-domain analog signal by a conventional digital-to-analog converter. The analog signal is then communicated over the transmission channel to the receiving modem, which reverses the process to recover the transmitted data. The non-ideal impulse response of the transmission channel of course distorts the transmitted signal. Accordingly, the signal received by the receiving modem will be a convolution of the analog output waveform with the impulse response of the transmission channel. Ideally, the DMT subchannels in the received signal are orthogonal so that the modulating data can be retrieved from the transmitted signal by a Discrete Fourier Transform (DFT) demodulation, under the assumption that convolution in the time domain corresponds to multiplication in the frequency domain.
While DMT provides excellent transmission data rates over modest communications facilities such as twisted-pair wires, the IDFT modulation can result in a high peak-to-average ratio (PAR) of the signal amplitudes. The PAR is defined as the ratio of the peak power level, for a sample, to the average power level over a sequence of samples. In the case of conventional DMT modulation, the amplitude of the time domain signal from the IDFT has a probability distribution function that has substantially a Gaussian shape. This Gaussian distribution of the signal amplitudes indicates the possibility that some time-domain samples may have amplitudes that are very high, as compared with the average sample amplitude. The resulting PAR is therefore much higher for DMT signals than for single-channel signals, because of the probability that the additive DMT peaks can overlay one another to result in an extremely large amplitude time-domain sample.
The high PAR for conventional DMT signals presents significant constraints on the transmission circuitry, and can greatly complicate the analog circuitry required for high fidelity transmission. For example, a high PAR translates into a large dynamic range at the inputs of digital-to-analog and analog-to-digital converters, necessitating a large number of bits of resolution, and the associated extreme cost and complexity. Filters and amplifiers must also become more complex and costly in order to handle both the high peak amplitudes and also the resolution required for the vast majority of the samples having lower amplitude. In addition, the high PAR results in much higher power consumption in the communications circuits, further increasing the cost of the circuits and systems used for DMT transmission and receipt, particularly those circuits often referred to as the analog front end (AFE).
A common approach to controlling the PAR in DMT transmission is to clip amplitudes that exceed a selected threshold. This clipping obviously results in loss of signal. Clipping effectively introduces an impulse at the clipped sample in the time domain signal, having the negative of the amplitude being clipped. As known in the art, a time-domain impulse corresponds to additive noise across all subchannels in the frequency domain, and thus clipping effectively reduces the signal-to-noise ratio for all subchannels in the modulated signal. In addition, the use of clipping requires a difficult tradeoff. Clipping to a relatively low amplitude threshold reduces circuit complexity and power dissipation, but greatly increases the probability of clipping; on the other hand, clipping at a high amplitude threshold decreases the probability of clipping but increases circuit complexity and cost. If the average power of the signal is kept small, so that the peak amplitude remains within the dynamic range of the analog circuitry, the signal amplifiers are operating in an inefficient operating state; conversely, the amplifier efficiency can be improved by raising the average power only by increasing the probability of clipping.
Various approaches have thus been developed to reduce the PAR of DMT signals to minimize the number of samples that require clipping. According to one class of techniques, DMT symbols are coded so that the resulting code words reside in the set of DMT symbols that reside below the desired PAR amplitude threshold. These techniques necessitate a loss of data rate, because of the coding overhead that results.
Another approach effects an invertible transformation on the transmitted signal, such as a phase rotation for certain subchannels, to reduce the probability that the PAR amplitude threshold is exceeded. Assuming the probability of the original signal exceeding the PAR threshold to be low, the probability that both the original signal and also the transformed signal will exceed the threshold will be approximately the square of the low probability for the original signal, which greatly reduces the extent of clipping. In this approach, a control signal is communicated to the receiver to identify the transformation, so that the receiver can apply the inverting transformation, as necessary, and recover the original signal.
Another approach estimates and corrects the effects of clipping at the receiver. As described in European Patent Application publication EP 0957 615 A2, published Nov. 17, 1999 and incorporated by this reference, an estimate of the clipping error is generated at the receiver, and is used to reconstruct a frequency domain compensation signal that is applied to the received signal, to remove the effects of any clipping.
A method of reducing the PAR in DMT transmissions without involving a loss of data rate is described in Gatherer and Polley, “Controlling clipping probability in DMT transmission”, Proceedings of the Asilomar Conference on Signals, Systems, and Computers, (1997), pp. 578-584, incorporated herein by this reference. As noted above, one function carried out in the training sequence on initiation of a DSL session determines the number of bits per symbol (i.e., the bit loading) assigned to each subchannel. After bit loading, it is common for a number of subchannels (typically at higher frequencies) to remain unloaded, carrying no data symbols at all. In the Gatherer and Polley article, the PAR is reduced by using these unloaded subchannels to carry a “signal” that contains no payload, but that has the effect of reducing the amplitude of the time domain signal to below the PAR amplitude threshold, in most cases.
In summary, the Gatherer and Polley method performs an iterative process to derive the symbols for the unloaded subchannels. In short, an initial trial value (possibly zero) of the unloaded subchannel signal is added, in the time-domain, to the time-domain signal after the IDFT. A nonlinear function corresponding to the clipping amplifier is applied to the summed signal; if no clipping results (i.e., if none of the signal elements change), the current trial value of the unloaded subchannel signal is kept as part of the signal. If, on the other hand, the nonlinear clipping amplifier function indicates clipping, the clipping is used to determine a new trial signal for the unloaded subchannels, and the process repeated until clipping does not occur.
Referring now to FIG. 1a, an example of transmission of a DMT signal over a DSL communication system according to the Gatherer and Polley article will now be described. Transmitting modem 10 receives an input bitstream that is to be transmitted to a receiving modem over a transmission channel. This input bitstream is a serial stream of binary digits, in the appropriate format as produced by the data source, and is received by bit-to-symbol encoder 11 in transmitting modem 10. Encoder 11 groups the bits in the input bitstream into multiple-bit symbols that are used to modulate the DMT subchannels. The number of bits in each subchannel varies according to the bit loading assigned to each subchannel in the initialization of the communication session, as known in the art. In addition, encoder 11 may also use error correction coding, such as Reed-Solomon coding, for error detection and correction purposes; other types of coding, such as trellis, turbo, or LDPC coding, may also be applied for additional signal-to-noise ratio improvement. The symbols generated by encoder 11 are typically complex symbols, including both amplitude and phase information, and correspond to points in the appropriate modulation constellation (e.g., quadrature amplitude modulation, or QAM).
The encoded symbols are then applied to inverse Discrete Fourier Transform (IDFT) (also referred to as inverse Fast Fourier Transform (IFFT)), function 12. IDFT function 12 associates each input symbol with one subchannel in the transmission frequency band, and generates a corresponding number of time domain symbol samples according to the Fourier transform. These time domain symbol samples are then converted into a serial stream of samples by parallel-to-serial converter 13. Functions 11 through 13 thus convert the input digital bitstream into a serial sequence of symbol values representative of the sum of a number of modulated subchannel carrier frequencies, the modulation indicative of the various data values. Typically, N/2 unique complex symbols (and its N/2 conjugate symmetric symbols) in the frequency domain will be transformed by IDFT function 12 into a block of N real-valued time domain samples.
As known in the art, function 14 adds a cyclic prefix to each block of serial samples presented by parallel-to-serial converter 13, by copying a selected number of sample values from the end of the block, and prepending the copy to the beginning of the block. The cyclic prefix has the effect of limiting intersymbol interference (ISI) due to energy from a previous symbol spreading into the next symbol due to the channel response. The cyclic prefix causes the datastream to appear to be periodic over a block of N of the N+P samples, where P is the length of the prefix, so that the equivalence between frequency domain multiplication and time-domain convolution is valid.
Upsampling function 15, and digital filter 16, then process the digital datastream in the conventional manner. As known in the art, upsampling function doubles or quadruples (or applies any multiple) the datastream to increase the sample rate, by inserting zero-value samples between each actual signal sample. Digital filter 16 may include such operations as a digital low pass filter for removing image components, and digital high pass filtering to eliminate POTS-band or ISDN interference. The digitally-filtered datastream signal is then converted into the analog domain, by digital-to-analog converter 17. Analog filtering (not shown) may then be performed on the output analog signal, such filtering typically including at least a low-pass filter. The analog signal is then amplified by amplifier 18 which, according to this embodiment of the invention, includes a clipping function, such as a hardlimiting clipping function that limits the amplitude to a maximum (both positive and negative polarities). As described in U.S. Pat. No. 6,226,322, digital-to-analog converter 17, amplifier 18, and any analog filtering, may be implemented in coder/decoder (codec) integrated circuit in transmitting modem 10 (FIG. 2).
The amplified analog output is then applied to a transmission channel, for forwarding to a receiving modem. According to conventional ADSL technology, the transmission channel consists of some length of conventional twisted-pair wires. In general, the receiving modem (not shown) reverses the processes performed by transmitting modem 10 to recover the input bitstream as the transmitted communication.
An example of the hardlimiting clipping function applied by amplifier 18 in his conventional transmission system is illustrated in FIG. 1b. Considering the input to amplifier 18 as sampled analog signal xs(n), amplifier 18 generates an output signal corresponding to the function ƒ(xs(n)), as shown in FIG. 1b. This function ƒ(xs(n)) can effectively be expressed as:       f    ⁡          (                        x          s                ⁡                  (          n          )                    )        =      {                                                    ⁢                                          -                M                            ,                                                                        ⁢                                          for                ⁢                                                                   ⁢                                                      Bx                    s                                    ⁡                                      (                    n                    )                                                              <                              -                M                                                                                                                    Bx                s                            ⁡                              (                n                )                                      ,                                                            ⁢                                          for                ⁢                                                                   ⁢                                                                                              Bx                      s                                        ⁡                                          (                      n                      )                                                                                                    <              M                                                                                    ⁢                          M              ,                                                                        ⁢                                          for                ⁢                                                                   ⁢                                                      Bx                    s                                    ⁡                                      (                    n                    )                                                              >                              -                M                                                        where B is the gain of amplifier 18, and where M is the maximum output magnitude of amplifier 18, as shown in FIG. 1b. As discussed above, each time the amplitude of a sample of signal xs(n) exceeds the clipping threshold |Bxs(n)|, data may be lost from the payload signal; alternatively, if the average power is held to be low enough to effectively avoid clipping, amplifier 18 will not be operating efficiently, and resolution in the transmitted signal will also be compromised.
According to the Gatherer and Polley method, unloaded channel encoding function 19 generates symbols that are assigned to unloaded subchannels in order to reduce the likelihood of clipping, by reducing the peak-to-average ratio (PAR) of the transmitted signal. A clip prevention signal Xc can be derived that is orthogonal to frequency-domain payload signal Xs, by assigning clip prevention signal Xc to subchannels where payload signal Xs is zero. An indicator matrix G can thus be derived as a diagonal matrix with ones corresponding to unloaded subchannels, and zeroes elsewhere. This indicator matrix G will thus have the properties:GXs=0GXc=Xcindicating that signals Xc and Xs are orthogonal to one another.
To reduce the peak amplitude of payload Xs after IDFT and D/A conversion, clip prevention signal Xc is selected to maintain payload signal Xs below the clipping threshold:ƒ(xs+xc)−(xs+xc)=0in the time domain, where xs=FHXs, FH being the inverse DFT operator (and F being the DFT operator). In the frequency domain, one may rewrite this relationship as: ƒ(FHXs+FHXc)−(FHXs+FHXc)=0One may readily solve for clip prevention signal Xc in the frequency domain by:Xc=Fƒ(FHXs+FHXc)−Xs.The orthogonality constraint between payload signal Xs and clip prevention signal Xc is enforced using the indicator matrix G:                               X          c                =                              GX            c                    =                                    GFf              ⁡                              (                                                                            F                      H                                        ⁢                                          X                      s                                                        +                                                            F                      H                                        ⁢                                          X                      c                                                                      )                                      -                          GX              s                                                              =                  GFf          ⁡                      (                                                            F                  H                                ⁢                                  X                  s                                            +                                                F                  H                                ⁢                                  X                  c                                                      )                              According to the Gatherer and Polley article, the clip prevention signal Xc is solved for using the Projection Onto Convex Sets (POCS) method. For example, an iterative method can be used to solve for the clip prevention signal Xc                 1. Start with an initial trial value for clip prevention signal Xc (e.g., Xc=0);        2. Form the time domain signal xs+xc=FHXs+FHXc;        3. Apply the nonlinear clipping function to the time domain signal xs+xc and determine whether any elements change (i.e., are clipped). If not, the current trial value of clip prevention signal Xc is adequate.        4. If clipping occurred, perform a DFT of the clipped time domain signal xs+xc and form a new trial value for clip prevention signal Xc, using the above equation including the indicator function, and repeat the process.An alternative approach, according to the Gatherer and Polley method, is to perform the step of forming a new trial value for the clip prevention signal xs in the time domain, using a vector of precomputed values and no additional transforms. This is accomplished by performing an IDFT of the expression for the clip prevention signal Xc, and then precalculating a shaping matrix S=FHGF that is applied to the clips of the clipped time domain signal xs+xc to be added to the prior trial value of clip prevention signal xc to produce the next trial value. The shaping matrix need only be calculated once for a given indicator matrix G, and the time domain transform xs=FHXs need only be performed once, according to this time-domain update approach. In this approach, the resulting time-domain clip prevention signal xc is added in after IDFT function 12, as shown in FIG. 1a.         
A particular benefit of the Gatherer and Polley method is that the receiver need not transform the signal, and that no data rate is lost. The modifying signal is applied by the transmitter only affects unloaded subchannels, and thus is not considered by the receiver in demodulating the transmitted signal. Indeed, the payload portion in the loaded subchannels are not modified in any way.